%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP107^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:46:59 PM UTC 2025
% Result : Theorem 22.99s 23.10s
% Output : Proof 22.99s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_partia1993116613t_unit,type,
partia1993116613t_unit: $tType ).
thf(ty_partia539144763t_unit,type,
partia539144763t_unit: $tType ).
thf(ty_partia1833973666xt_a_b,type,
partia1833973666xt_a_b: $tType ).
thf(ty_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(ty_set_a,type,
set_a: $tType ).
thf(ty_r3,type,
r3: a ).
thf(ty_s,type,
s: set_a ).
thf(ty_mult_a_ring_ext_a_b,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(ty_r,type,
r: partia1833973666xt_a_b ).
thf(ty_locali1944243560ac_a_b,type,
locali1944243560ac_a_b: partia1833973666xt_a_b > set_a > partia539144763t_unit ).
thf(ty_mult_s977248631t_unit,type,
mult_s977248631t_unit: partia539144763t_unit > set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(ty_s3,type,
s3: a ).
thf(ty_r2,type,
r2: a ).
thf(ty_s2,type,
s2: a ).
thf(ty_rel,type,
rel: partia1993116613t_unit ).
thf(ty_locali1170246543t_unit,type,
locali1170246543t_unit: partia1993116613t_unit > a > a > set_Product_prod_a_a ).
thf(sP1,plain,
( sP1
<=> ( ( locali1170246543t_unit @ rel @ r2 @ s2 )
= ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( rel = rel ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: set_Product_prod_a_a,X2: set_Product_prod_a_a] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: set_Product_prod_a_a] :
( ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) )
= X1 )
=> ( X1
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) )
=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( locali1944243560ac_a_b @ r @ s )
= ( locali1944243560ac_a_b @ r @ s ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( locali1170246543t_unit @ rel @ r3 @ s3 )
= ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) )
=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: set_Product_prod_a_a] :
( ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= X1 )
=> ( X1
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( mult_a_ring_ext_a_b @ r @ s2 @ s3 )
= ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP9
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) )
= ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( mult_a_ring_ext_a_b @ r @ r2 @ r3 )
= ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(conj_0,conjecture,
sP17 ).
thf(h0,negated_conjecture,
~ sP17,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP16
| sP14
| ~ sP20
| ~ sP3 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
sP8,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
sP1,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP15
| sP20
| ~ sP11
| ~ sP7 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( sP9
| ~ sP2
| ~ sP21
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP19
| ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP5
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
sP10,
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP3
| ~ sP8
| ~ sP1
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
sP2,
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP12
| ~ sP14
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP6
| ~ sP15
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP13
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP4
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
sP4,
inference(eq_sym,[status(thm)],[]) ).
thf(fact_0_f3,axiom,
sP21 ).
thf(fact_1_f4,axiom,
sP18 ).
thf(fact_3_f1,axiom,
sP16 ).
thf(fact_4_f2,axiom,
sP15 ).
thf(18,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,fact_0_f3,fact_1_f4,fact_3_f1,fact_4_f2,h0]) ).
thf(0,theorem,
sP17,
inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ITP107^1 : TPTP v9.2.0. Released v7.5.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:36:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 22.99/23.10 % SZS status Theorem
% 22.99/23.10 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 22.99/23.10 % Inferences: 907
% 22.99/23.10 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------